Welcome to the forum. Thanks for your question. I can help.
You don't describe the sexual exposure you are concerned about, but it sounds like you may have been overtested. It is rare that all those tests are necessary after a single exposure. That's especially the case for hepatitis testing. (And contrary to popular beliefs, hepatitis C isn't sexually transmitted at all, except perhaps between some gay men who participate in traumatic/bloody sexual practices involving the rectum.)
To your specific questions:
1) Your negative HIV test results are conclusive. Here is a thread from just yesterday, explaining why tests earlier than 3 months are usually conclusive despite official advice otherwise:
http://www.medhelp.org/posts/show/1704700
2) The syphilis blood tests are solid after 6 weeks (about 42 days). HSV testing needs to be delayed to 3 months, sometimes even 4 months after exposure. But the chance you caught HSV is probably low. I don't recommend any more testing unless you have had herpes symptoms or your partner is known to be infected.
3) Your hepatitis tests were unnecessary, but the results are reliable.
4) This can have no effect on your test results for HIV or anything else.
5) There are no common illnesses or medications that have any effect on HIV test reliability.
All things considered, you really should not be worried at all. But let me know if there is anything you don't understand.
Regards-- HHH, MD